Stochastic differential equations (SDEs) on compact foliated spaces were introduced a few years ago. As a corollary, a leafwise Brownian motion on a compact foliated space was obtained as a solution to an SDE. In this work we construct stochastic flows associated with the SDEs by using rough path theory, which is something like a 'deterministic version' of Ito's SDE theory.
This is joint work with Kiyotaka Suzaki.
Yuzuru Inahama is a Professor in the Department of Mathematical Sciences at Kyushu University in Japan. His research interests include stochastic analysis and its applications, in particular, rough path theory, Malliavin calculus and stochastic differential equations.